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PDE-constrained shape registration to characterize biological growth and morphogenesis from imaging data
Aishwarya Pawar1, Linlin Li2, Arun K Gosain3
1School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, 47907, Indiana, USA.
Engineering with Computers
|December 4, 2023
Summary
This study introduces a novel algorithm for shape registration, enabling precise tracking of biological tissue deformation and growth. The method enhances understanding of complex biological processes and medical applications involving tissue changes.
Area of Science:
- Computational biology
- Biomedical engineering
- Medical imaging analysis
Background:
- Shape registration aligns geometries using spatial transformations.
- Previous work utilized 3D tensor product B-spline basis functions for spatial interpolation.
Purpose of the Study:
- To develop a PDE-constrained algorithm for shape registration that quantifies biological tissue deformation and growth.
- To analyze tissue expansion in processes like zebrafish embryo epiboly and skin reconstruction.
Main Methods:
- The algorithm models deformation using B-spline control point movement and an implicit shape function.
- Deformation gradients are decomposed into growth and elastic components.
- A total energy functional, including shape similarity and elastic energy, is minimized.
Main Results:
- The framework successfully quantifies tissue deformation and growth.
- Applied to zebrafish embryo epiboly and skin reconstruction, demonstrating its utility.
- Provides a method to analyze extreme tissue deformations over time.
Conclusions:
- The proposed PDE-constrained shape registration method offers a robust approach for studying biological tissue dynamics.
- This technique is expected to advance the understanding of various biological and medical scenarios involving significant tissue deformation.
- Enables quantitative analysis of growth and elastic properties in biological tissues.
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